An isotope of 'parent' is produced, when its nucleus loses

Options

A. One `alpha-`particle
B. One `beta-`particle
C. One `alpha` and two `beta`-particles
D. One `beta` and two `alpha-`particles

Explanation

To solve the question, we need to determine what happens when a parent isotope loses particles from its nucleus and how that affects its identity as an isotope.

### Step-by-Step Solution:

1. **Understanding Isotopes**: An isotope of an element has the same atomic number (number of protons) but a different mass number (number of neutrons). This means that when a parent isotope transforms into a new isotope, the atomic number must remain unchanged.

2. **Identifying Particle Loss**: The question asks us to identify what type of particle can be lost from the nucleus without changing the atomic number. The common particles emitted during radioactive decay are alpha particles (α), beta particles (β), and gamma rays (γ).

3. **Analyzing the Options**:
- **Option 1: +2 alpha, 4**: An alpha particle consists of 2 protons and 2 neutrons. Losing an alpha particle would decrease the atomic number by 2, which is not acceptable for producing an isotope of the parent.
- **Option 2: -1 beta, 0**: A beta particle is an electron (or positron) emitted from the nucleus. Losing a beta particle would change the atomic number by +1 (if it’s a beta minus decay), which also does not maintain the identity of the parent isotope.
- **Option 3: 1 alpha particle and 2 beta particles**: This option suggests losing 1 alpha particle (which decreases the atomic number by 2) and 2 beta particles (which would increase the atomic number by 2). The net effect on the atomic number is zero, thus maintaining the identity of the parent isotope.
- **Option 4: 1 beta particle and 2 alpha particles**: This option would decrease the atomic number significantly (by 4 from the alpha particles and increase by 1 from the beta particle), which is not acceptable.

4. **Conclusion**: The only option that results in the atomic number remaining unchanged while allowing for a change in mass number is **Option 3: 1 alpha particle and 2 beta particles**.

### Final Answer:
**Option 3: 1 alpha particle and 2 beta particles.**

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